Wednesday, October 19, 2005

Buying in for the Maximum at NL: Yay or Nay?

Been on a very nice little degenerate tear for the last few weeks or so. I mean, wait, no, shhh... I've been running horribly, gambling, gods, very horribly. Do not smite me down, do not smite me down...

All of you 7 Card Stud players have my undying respect these days. I've been slowly working my way through the S&M Boys' Seven-Card Stud for Advanced Players, mainly just for kicks, as I can't remember the last time I actually played Stud. While it makes perfect sense that Hold 'Em would fuel the poker craze, due to its more simplistic nature, it's a shame that Stud got shoved over into the dark corner, as it's definitely much more nuanced and difficult to play well.

Daniel Negreanu has an interesting post recently at his blog (scroll down a bit to get to the poker part) about buying in for a massive amount at a no maximum buy-in $1/2 NL table, and the advantage of doing so. His hypothetical example involves you, a good player, sitting down at the table and buying in for $200, while a horrible player sits down at the same time and and buys in for $1,000,000. It's not spelled out, but the implied situation is that it's a full table after the two of you sit down, not shorthanded, not headsup, and that the other players bought in for "normal" amounts.

Does the horrible player, due solely to the size of his buy-in (which easily covers the entire table) now have an overall advantage over you and your piddling little $200?

If you answered no, congratulations, here's a cookie.

I have to admit that my gut reaction was that yes, of course he has an advantage, and that you'd be insane to claim otherwise. If you only have $200 to work with he could absolutely run over you, putting you all-in constantly, coming over the top of any raise, and the size of his stack would eventually break you, no matter how poorly he played.

Your only concern when you sit down is that you get full value for your $200 in a +EV situation. That's it. The size of the horrible player's stack (or any other stack at the table) only affects your ability to get full value to the extent that it must be equal to or larger than your own.

You still retain every advantage you have, being a better player. Odds-wise, you're still a favorite to make more money than the horrible player while you sit at the table. Could you have increased your profitability and extracted more money by initially buying in for more than $200? Well, of course. But that's always true of any gambling situation, when viewed in hindsight after you catch a monster hand/hit a trifecta/get dealt blackjack, and isn't really the point.

The key here, which is fairly obvious yet a bit sneaky, is that you can simply get up and stop playing at any point you want. If this were a tournament or a sit and go, then yes, of course, the huge stack has a huge advantage. But in a cash game it's completely different, as your goal isn't to acquire every chip at the table but to get full value for your buy-in when you decide to put it at risk. All that matters is that your opponent has a stack of sufficient size to allow you to do that. Anything they have over and above the value of your stack is completely tangential. The fact that you can get up and leave at any point robs the big stack of much of its heft.

Daniel continues to the following conclusions:

"If you buy in for the minimum, it makes the correct strategy very simple. If you buy in for the most, it will force you to make more difficult decisions."

He goes on to give the following example:

"You raise to $30 with AA and get three callers. The flop comes 9c 6d 2s and you bet your last $50. That's a no brainer right? Well, what if you had $20,000 in front of you? You bet the $50 and a player raises you $200 more. Now what do you do? It's more difficult isn't it?

You aren't going to stick the whole $20,000 in are you? No, you might raise to $1000 or so. Say you do, and now your opponent raises you back $5000 more? Do you fold? Do you call? Tough isn't it?"

Which, again, is interesting, especially the first quoted part, as it flies a bit in the face of conventional wisdom. He does advocate that if you're the best player at the table (and you can do so), you should buy in for an amount that covers the table. Not because the huge stack carries any inherent advantage, but because it ensures that you likely won't ever have to go all-in. The more play there is in a hand (i.e. the more opportunity there is to raise or re-raise without shoving all-in), the better for you. If you're the best player, you prefer many decisions for lesser sums of money to be made, instead of fewer decisions for larger sums of money, as your skill exerts itself more insistently with each additional decision made.

It's the converse of the above that's interesting, as far as intentionally buying in for less than the maximum. Let's say you're a good NL player and you have $200 in your account at your favorite online poker site. You're ready to play some cards at the $.50/1 NL tables, which have a minimum buy-on of $50 and a maximum buy-in of $200.

General wisdom (I think) would have you finding the juiciest table and buying in for the maximum of $200, with the thinking being that you need to buy-in for the maximum in order to extract the most value from big hands that you patiently wait for, etc.

Following the above logic, though, you could make a very good argument that you should instead buy-in to two different tables, each for $100. You're still just as likely to get full value for your $200, and you're going to be presented with approximately twice the number of decisions to be made. Since you're a good player, this is a good thing, as the extra decisions give you more chances to shine. Because of the maximum buy-in limit, you can't cover the table anyway, so buying in for more than $100 doesn't greatly reduce the odds that you'll be all-in at some point.

What if you had $10,000 in the same account, though? Should you still play two tables, buying in at $100 each, or should you buy in for $200 at both tables?

That's where it gets truly interesting and speculative. If risk of ruin (essentially the percentage of the time that normal variance will wipe out your entire bankroll) isn't an issue, then yes, you should probably buy in for $200 at both tables. While buying in for less than the maximum may not put you at any real disadvantage, the only potential advantage that buying in for less gives is that it simplifies decision making at times. But even that's a paltry advantage, since if you're a good player you should be welcoming the opportunity to make tough decisions.

The more interesting extension, though, is the idea that instead of buying into two $.50/$1 tables for $200 each, you should instead use the same money ($400) to buy-in for less than maximum at a bigger game. If buying in for less than the maximum has no effect on your relative advantage/disadvantage at NL, you should therefore be much more willing to take shots at bigger games. Assuming, of course, that what was previously preventing you from doing so was the fact that you were waiting to be bankrolled to the point that you could comfortably buy in for the maximum. If other issues are holding you back then it's a whole other ball of wax.

Much of this may be very common-sensical to many of you, and my apologies for the extended babbling if so. I just thought it was pretty interesting and eye-opening, as I've always operated under the notion that buying in for less than the table maximum at NL/PL was a clear mistake, and now I'm not sure that's the case. I won't go so far as to claim there's any inherent advantage in doing so, other than freeing you up to take shots at bigger games, but there don't appear to be as many disadvantages as I'd previously thought.

4 comments:

I have read some other ideas of buying in at less than the max as a form of personal stop loss. This also seems to be a slight form of that, when your good decision that gets sucked out on does not hurt the bankroll as much.

Hey. I admire your posts and your tangent is sound.But the context of Negreanu's argument is a bit off. He was responding to criticism of why he bought in for $125,000 at a $5/10 NL table at the Wynn recently and some people on his forum said that was unfair.So he's responding to their criticism with an argument about what if a horrible player buys in for an extravagant sum. That shouldn't make much difference to you as a good player, right?His argument is deflection -- he's one of the top players in the world, so this should cause some worry to you, particularly if you're not a very good player, and he's sitting at your table with tens of thousands more chips than you have.It reminds me of the account of Bobby Baldwin raising a guy who had always wanted to play him $36,000 when they both had the same nut hand. The guy almost folded.Wielded by an expert, a big buy-in is a dangerous weapon and in NL you use it to extract the most psychological pressure possible on opponents every time they contest you. It's the right way to play, ala the Theory of Poker. Make your opponent make more mistakes than you and you will come out ahead. It could be construed as unfair, but life seems to be inherently unfair. You may lose your shirt by being horribly outgunned against a pro but hopefully you'll learn something valuable in the process.

One thing that I disagree with regarding Negreanu's comment is the impact being short stacked in a NLHE cash game has on your odds. If you have a small stack in comparison with everyone at the table (but not compared to the blinds), I would assume (or have witnessed behavior) that you'll have more individuals in a hand. While Daniel may be right regarding AA heads-up, any hand drops in value playing two, three, or four opponents. The other behavior that seems real is the over-the-top play by large stacks, whether you're a raiser or a limper. This means that rather than seeing a flop you're required to put in half-2/3 of your stack, virtually pot-committing you. I would suggest that Daniel try the opposite approach--go to the Bellagio, buy-in at the $2/5NLHE for $150 when everyone else has a stack of $700-$2000. Then he can talk about this.